Quark Imaging at JLab 12 GeV and beyond (2) Compton Scattering Tanja Horn π , K, etc. Jefferson Lab Known π , process K, GP etc. D ~ ~ H H E E HUGS, Newport News, VA 11 June 2009 Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009 Tanja Horn, CUA Colloquium 1
Quark Imaging • Wigner quantum phase space distributions provide a simultaneous, correlated, 3-dimensional description of both the position and momentum. • They are the closest analogue to a classical phase space density allowed by the uncertainty principle. x = 0.01 x = 0.40 x = 0.70 Pictures show transverse plane for different quark momentum fractions x Interference pattern Wigner distributions provide the language for the Generalized Parton Distributions (GPDs), which allow us to create a complete map of the behaviour of partons (quarks and gluons) inside of the nucleon. Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009 Tanja Horn, CUA Colloquium 2
Probing GPDs in the Nucleon • We need to find a process, which we can describe by factorizing it into: – a known part that we can calculate, and – one that contains the information we are after e k' Known process * • For some reactions it has been proven that such factorization is possible, but only under very GPD extreme conditions p' – p In order to use them, one needs to show that they are applicable in “real life” • A decisive test is to look at the scaling of the cross section (interaction probability) as a function of Q 2 , and see if it follows the QCD prediction for scattering from a cluster of point-like objects Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009 3
Feasibility ↔ Measurement π , K, etc. • Exclusive meson production adds flavor to Known quark imaging studies π , process – But one needs to test various pre-requisites K, GP – etc. Demonstrate that, e.g., QCD factorization applies D ~ ~ H H E E • What about other exclusive processes like Compton scattering? – Factorization easier to achieve – But cannot learn about flavor Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009 4
Compton Scattering and Factorization Q 2 independent -t • Beam-spin-dependent BH-DVCS interference cross sections are independent of Q 2 consistent with an early approach to Q 2 scaling Leading twist QCD factorization may be applicable already at low Q 2 of a few GeV 2 Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009 5
Compton Scattering * * p p • Real Compton Scattering – Both photons are real γ * γ • Deeply Virtual Compton Scattering (DVCS) – Outgoing photon is real – Simplest and cleanest process probing GPDs • Timelike Compton Scattering (TCS) – Incoming photon is real TCS DVCS – Complementary to DVCS. Allows more reliable GPD extraction, and interesting model comparisons. • Double DVCS – Both photons are virtual – The general Compton process can provide most information – Experimentally challenging Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009 6
Experimental Access to GPDs: DVCS • Using a polarized beam on an unpolarized target, two observables can be measured: 4 * p p d 2 2 BH BH DVC S DVCS 2 Re T T T T 2 dx dQ dtd B • γ * has a large spacelike virtuality • -t is small 4 4 d d 2 2 BH DVCS DVCS DVCS 2 Im T T T T 2 2 2 2 x [Q /y(s - m - M )] 2 dx dQ d d t ep B l p B ( ) /( ) y q p k p
Timelike Compton Scattering p p l l Bethe-Heitler (BH) TCS 2 + + , l e • The main TCS observable is the angular distribution of a photoproduced lepton pair • The hard scale of the process is given by its invariant mass • Access to the Compton amplitude is possible through interference with BH • GPDs may be extracted from the Compton amplitude – The restrictions on t are like in DVCS Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009 8
DVCS Cross Section Challenges 4 σ 4 σ d d BH DVCS DVCS DVCS 2 2 2T Im(T ) | T | | T | 2 dtd φ dx dQ B Assume this is small C. Munoz Camacho et al ., PRL 97 (2006) Φ γγ (deg) d σ is much larger than the BH contribution • Relative Beam Spin Asymmetry (BSA=d 4 Σ /d 4 σ ) is not simply the imaginary part of • BH-DVCS interference divided by BH cross section Does DVCS 2 term contribute more than expected? – Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009 9
DVCS Cross Section Puzzles J.M. Laget, Phys. Rev. C 76 : 052201 (2007) • Compton scattering is related to vector meson production by unitarity • Coupling to vector meson production channels may give the dominant contribution to DVCS – Explains the unexpected large DVCS unpolarized cross section, spin and charge asymmetries without explicitly invoking GPDs Suggests that partonic description may not yet be applicable Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009 10
Why TCS in addition to DVCS? Pros • Real part of amplitude can be measured with better systematics • TCS and DVCS amplitudes are equivalent only to leading order – at finite Q 2 , data on both reduces model dependence of GPD extraction • TCS asymmetries are easy to compare directly with GPD models – Polyakov-Weiss D-term Cons • Cross section smaller than for DVCS – enhancement through interference with Bethe-Heitler always needed Resonances in timelike final state limit Q '2 coverage • Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009 11
Spatial Imaging through Elastic Form Factors • The elastic scattering cross section can be factorized into that of a point object and a part that gives information about the spatial distribution of the constituents 2 2 d σ d σ | F(Q ) | d Ω d Ω point object • The spatial distribution (form factor) is a Fourier transform of the charge distribution 3 2 iq r/ ρ(r)e F(Q ) d r • Spin 0 mesons ( π + , K + ) have electric charge form factor only – Spin ½ nucleons have electric and magnetic form factors Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009 12
Momentum Imaging through Deep Inelastic Scattering • Cross section can be factorized into that of a point object and a part that gives information about the momentum distribution of the constituents in the nucleon 1 p 2 2 2 2 2 2 2 3 σ 4 ππ d F (x, Q ) Mxy y Q /E 2 1 y 2 4 2 x 2E dQ dx Q 2(1 R(x, Q ) e ’ (E’,p’) e (E,p) • The longitudinal momentum distribution is given by the quark distribution functions ( ν , Q 2 ) γ * u u u 2 F F (x) x e (q (x) q (x) ) d d 2 2 i i i i u • By measuring quark distribution functions, one cannot say anything about the momentum fraction perpendicular to the direction of motion Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009 13
Mapping Nucleon Structure Form Factors Parton Distributions (PDFs) Spatial size of the nucleon Longitudinal momentum distribution • How can we learn about the transverse spatial distribution of partons? • Processes for this other than elastic and inclusive scattering? Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009 14
Mapping Nucleon Structure Form Factors Parton Distributions (PDFs) Spatial size of the nucleon Longitudinal momentum distribution Generalized Parton Distributions (GPDs) Transverse spatial distribution of quarks with longitudinal momentum fraction x GPDs “unify” form factors and parton distributions Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009 15
Limits of GPDs Q 2 ~ x Bj x x Form Factors PDFs t 1 1 ~ , q g q q q q ( , 0 , 0 ) ( ) ξ, ξ, H x t q x dx H (x, t) F (t) dx H (x, t) g (t) 1 A ~ 1 1 q , g ( , 0 , 0 ) ( ) H x t q x 1 1 ~ q q q q ξ, ξ, dx E (x, t) F (t) dx E (x, t) h (t) 2 A 1 1 E ~ : nucleon helicity flip: don’t appear in DIS , E A good determination of the form factors is essential for modeling GPDs, in particular their t-dependence 16 Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009
Tomography of the Nucleon Deep Inelastic Scattering Compton γ * γ * γ γ (x+ ξ )P (x- ξ )P xP xP ~ ~ H H E E Fourier transform Challenge: observables contain convolution integrals over x, Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009 17
Convolutions of GPDs • Summed over quark flavor and electric charge Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009 18
Probing GPDs through Compton scattering (Im, x = ) (|Re|) DVCS: spin asymmetries TCS: azimuthal asymmetry HERMES, CLAS, Hall A CLAS DVCS: charge asymmetry DIS: PDFs at ξ = 0 HERMES (|Re| 2 ) (Im, x ≠ ξ , x < | ξ | ) DVCS: cross sections DDVCS, CLAS12 ? H1, Hall A Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009 19
Revealing GPDs • Extraction of GPDs from experimental data requires: – Extensive experimental program – Phenomenological parameterizations of GPDs • Commonly used parameterizations use a factorized Ansatz for the t-dependence t – ~ x Regge parameterizations Tanja Horn, Quark imaging at JLab 12 GeV and beyond, HUGS 2009 20
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